Finite Group Databasebeta

← #29656314

Subgroups — #29656314

Order 15616.

918 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456199C211yesmaximal, characteristic
2#21455949C212yesmaximal
3#21445040C218yesmaximal, complemented
4#21444545C211yesmaximal, characteristic
5#21444266C212yesmaximal
6C2×Q82×C61C211yesmaximal, characteristic
7#16840319C2211yescharacteristic
8#16840130—22no—
9#16840112C2214yes—
10#16840092—22no—
11#16840047C2214yes—
12#16839972C2214yes—
13#16839918—22no—
14#16839867—24no—
15#16839819C2212yes—
16#16839771—22no—
17C4×#11758194C2211yescharacteristic
18#16839511C2214yes—
19Q8⋊#92418C2218yes—
20Q82×C61—22no—
21Q82×C61—24no—
22Q82×C61C2214yes—
23C2×C4⋊Q8×C61—22no—
24C2×C4⋊Q8×C61—22no—
25C2×C4⋊Q8×C61C2211yescharacteristic
26C2×C4×Q8×C61—22no—
27C2×C4×Q8×C61C2212yes—
28C2×#11758202—24no—
29C2×#11758194—21no—
30#14519777C2312yes—
31#14519769—21no—
32#14519756—22no—
33C4×Dic122—22no—
34#14519736—21no—
35#14519708—24no—
36C4⋊#92418C2314yes—
37#14519701—28no—
38#14519701—24no—
39#14519700—24no—
40C22⋊#92418—22no—
41#14519688—21no—
42#14519688—22no—
43C4×#92418C2312yes—
44C22×Q8×C61—22no—
45C22×Q8×C61D412yes—
46C22×Q8×C61D412yes—
47C4⋊Q8×C61—28no—
48C4⋊Q8×C61—28no—
49C4⋊Q8×C61—28no—
50C4⋊Q8×C61—28no—
51C4⋊Q8×C61—22no—
52C4⋊Q8×C61D412yes—
53C4⋊Q8×C61C2312yes—
54C4×Q8×C61—28no—
55C4×Q8×C61—28no—
56C4×Q8×C61—22no—
57C4×Q8×C61—22no—
58C4×Q8×C61D414yes—
59C4×Q8×C61C2314yes—
60C2×C4⋊C4×C61—24no—
61C2×C4⋊C4×C61—22no—
62C2×C4⋊C4×C61—22no—
63C2×C4⋊C4×C61D412yes—
64C2×C42×C61—22no—
65C2×C42×C61—22no—
66C2×C42×C61C2311yescharacteristic
67C2×Q8×C61—28no—
68C2×Q8×C61—28no—
69C2×Q8×C61—22no—
70C2×Q8×C61—22no—
71C2×Q8×C61—44no—
72C2×Q8×C61—84no—
73C2×Q8×C61C2×D414yes—
74C2×Q8×C61C2×D414yes—
75C22×C4×C61—22no—
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61C2×D412yes—
79C22×C4×C61C2×D411yescharacteristic
80C2×Dic122—22no—
81C4⋊C4×C61—216no—
82C4⋊C4×C61—24no—
83C4⋊C4×C61—24no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—24no—
86C4⋊C4×C61—24no—
87C4⋊C4×C61C2×D414yes—
88C42×C61—28no—
89C42×C61—24no—
90C42×C61—24no—
91C42×C61C2×D411yescharacteristic
92C42×C61C2×D412yes—
93C42×C61C2411yescharacteristic
94C22⋊Dic61—41no—
95#11758202—48no—
96C4⋊Dic61—22no—
97C4⋊Dic61—22no—
98#11758196—42no—
99C4×Dic61—41no—
100#11758194—42no—
101C2×#92418—22no—
102C2×#92418—24no—
103C23×C61#12011yescharacteristic
104Q8×C61—28no—
105Q8×C61—24no—
106Q8×C61—44no—
107Q8×C61—82no—
108Q8×C61—88no—
109Q8×C61#13718yes—
110C2×C4×C61—28no—
111C2×C4×C61—24no—
112C2×C4×C61—22no—
113C2×C4×C61—24no—
114C2×C4×C61—24no—
115C2×C4×C61—24no—
116C2×C4×C61—44no—
117C2×C4×C61—44no—
118C2×C4×C61#12011yescharacteristic
119C2×C4×C61#12012yes—
120C2×C4×C61C22×D411yescharacteristic
121C2×C4×C61C22×D412yes—
122C2×Dic61—42no—
123Dic122—44no—
124#92418—42no—
125#92418—44no—
126#18551—611nomaximal, Sylow
127C22×C61—22no—
128C22×C61#45512yes—
129C22×C61C2×#12011yescharacteristic
130C4×C61—28no—
131C4×C61—22no—
132C4×C61—21no—
133C4×C61—21no—
134C4×C61—44no—
135C4×C61—44no—
136C4×C61C2×#13714yes—
137Dic61—82no—
138C2×Q82D6111yescharacteristic
139#3139—611no—
140#3113—612no—
141#1645—618no—
142#1558—611no—
143#1491—612no—
144C2×C61—22no—
145C2×C61#300412yes—
146C2×C61C2×#45511yescharacteristic
147Q82—22no—
148Q82—24no—
149Q82C2×D6114yes—
150#533—611no—
151C2×C4⋊Q8—22no—
152C2×C4⋊Q8—22no—
153C2×C4⋊Q8C2×D6111yescharacteristic
154C2×C4×Q8—22no—
155C2×C4×Q8C2×D6112yes—
156#491—1222no—
157#487—614no—
158#483—1222no—
159#475—614no—
160#462—614no—
161#451—1222no—
162#441—1224no—
163#432—612no—
164#419—1222no—
165C4×M16—611no—
166#333—614no—
167Q8⋊C8—618no—
168C61#1855111yescharacteristic, complemented, Sylow
169C22×Q8—22no—
170C22×Q8C22⋊D6112yes—
171C22×Q8C22⋊D6112yes—
172C2×Q16—1224no—
173C2×M16—1221no—
174C4⋊Q8—28no—
175C4⋊Q8—28no—
176C4⋊Q8—28no—
177C4⋊Q8—28no—
178C4⋊Q8—22no—
179C4⋊Q8—612no—
180C4⋊Q8C22⋊D6112yes—
181C4⋊Q8C22×D6112yes—
182#125—1221no—
183C22⋊Q8—1222no—
184C4×Q8—28no—
185C4×Q8—28no—
186C4×Q8—22no—
187C4×Q8—22no—
188C4×Q8—1222no—
189C4×Q8C22⋊D6114yes—
190C4×Q8C22×D6114yes—
191#117—1221no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4C22⋊D6112yes—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42C22×D6111yescharacteristic
199#106—1224no—
200C4⋊C8—614no—
201#103—1228no—
202#103—1224no—
203#103—1224no—
204C22⋊C8—1222no—
205#97—1221no—
206#97—1222no—
207C4×C8—612no—
208C2×Q8—28no—
209C2×Q8—28no—
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—44no—
213C2×Q8—84no—
214C2×Q8—1222no—
215C2×Q8C2×C22⋊D6114yes—
216C2×Q8C2×C22⋊D6114yes—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4C2×C22⋊D6112yes—
221C22×C4C2×C22⋊D6111yescharacteristic
222Q16—2448no—
223M16—2442no—
224C2×C8—1222no—
225C2×C8—1224no—
226C4⋊C4—216no—
227C4⋊C4—24no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C4⋊C4—24no—
231C4⋊C4—22no—
232C4⋊C4—1222no—
233C4⋊C4—1222no—
234C4⋊C4—2442no—
235C4⋊C4C2×C22⋊D6114yes—
236C22⋊C4—2441no—
237C42—28no—
238C42—24no—
239C42—24no—
240C42—2441no—
241C42C2×C22⋊D6111yescharacteristic
242C42C2×C22⋊D6112yes—
243C42C23×D6111yescharacteristic
244C23#1451974611yescharacteristic
245Q8—28no—
246Q8—24no—
247Q8—44no—
248Q8—82no—
249Q8—88no—
250Q8—2444no—
251Q8#1451980818yes—
252C2×C4—28no—
253C2×C4—22no—
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—2442no—
261C2×C4#1451974612yes—
262C2×C4#1451974611yescharacteristic
263C2×C4C22×C22⋊D6111yescharacteristic
264C2×C4C22×C22⋊D6112yes—
265C8—2442no—
266C8—2444no—
267C22—22no—
268C22#1683994012yes—
269C22C2×#1451974611yescharacteristic
270C4—21no—
271C4—21no—
272C4—28no—
273C4—22no—
274C4—44no—
275C4—44no—
276C4—4882no—
277C4C2×#1451980814yes—
278C2—22no—
279C2#2145505312yes—
280C2C2×#1683994011yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×Q82×C61C2
socleC22×C61C2×#120
prime radicalC23×C61#120
hypercenterC2×Q82D61
hypocenterC61#18551
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×Q82

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21445040C2semidirect
168. C61#18551semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214561992
#214559492
#214450402
#214445452
#214442662
C2×Q82×C612
#1855161